The development of cryptography, public key cryptography in particular, was a
crucial factor responsible for the growth and popularization of computer
networks. It was responsible for appearance of demands as email, e-commerce,
digitals signature and certification. The proper use of cryptographic
techniques requires the development of efficient applications  capable
of running in all kind of devices witch more and more incorporates people's
lives. The generation of cryptographic keys is not only a critical
security operation but also a have high computational cost. This project has the goal
of studying cryptosystems and their theoretical basis and primality test, the
core element of the key generation process. It has an especial approach on implementing,
optimizing and performance analysis of Simplified Quadratic Frobenius Test, a
primality test from 2005 and under explored. The achieved results are positives
about the feasibility of reducing the computational cost of operation.